3. Vectors

If two velocity vectors are added using the component method, which of the following correctly describes how to find the magnitude of the resultant velocity vector $v_r$ given their components $v_{1x}$, $v_{1y}$, $v_{2x}$, and $v_{2y}$?

Given two vectors $A$ and $B$ with components $A=(3,4)$ and $B=(1,-2)$, what are the components of the vector $A+B$?

Given two vectors in a plane, how many distinct combinations (regardless of magnitude or direction) can sum to produce an arbitrary third vector?

Which of the following does not describe the process of adding vectors by components?

Suppose you have four vectors of equal magnitude: $\mathrm{Vector} A$ points along the positive $x$-axis, $\mathrm{Vector} B$ points along the positive $y$-axis, $\mathrm{Vector} C$ points at $45°$ above the $x$-axis (in the first quadrant), and $\mathrm{Vector} D$ points at $45°$ below the $x$-axis (in the fourth quadrant). Which pair of vectors, when added, will result in the largest positive $y$ component?

Given two vectors $A$ and $B$ with components $A=\left(3,4\right)$ and $B=\left(1,-,2\right)$, what is the single vector that represents $A+B$ when added by components?

Which of the following operations will not change a $\mathrm{vector}$?

A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference B - A

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference A - B

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector sum A + B

FIGURE P3.43 shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. How hard and in what direction must you pull on the third rope to keep the knot from moving? Give the direction as an angle below the negative x-axis.

A position vector in the first quadrant has an x-component of 6 m and a magnitude of 10 m. What is the value of its y-component?